How do you animate the Inception spinning top?
I have created a simple example for you.

First, the origin of the object must be at the tip of the totem.

In Edit mode, select the vertex end of the tip and press Shift+S to move the 3D cursor there.

Next, switch to Object mode and press Ctrl+Shift+Alt+C to move the origin to the 3D cursor.

You are now set up for origin.

Second, you need to edit the animation.

Notice the shape of the curve in the graph editor in GIF which I attached.

The Z axis, which is the rotation axis of the totem, is animated by linear interpolation.

Then apply a sine wave key animation that fades out to the X or Y axis.

I hope this helps.